Hmmm.... Don't think so... Even if you throw in the "worn out" factor... A 11/32 socket is significantly smaller than a 10 mm socket.
11 / 32 = 0.34375
1 inch = 25.4 mm
Therefore, 11/32" = 0.34375 x 25.4 = 8.73 mm
You just might be able to use a worn out 11/32 socket to remove a 9 mm bolt, but no go on a 10 mm bolt I am afraid...
Actually 3/8 is NOT "just a touch bigger than 10 mm." It is in fact smaller enough that even a worn out 3/8 socket will likely not fit on a 10 mm bolt.
3/8" = 3 / 8 x 25.4 = 9.525 mm.
Frankly is not 5, 6, 7, 8, 9, 10, 11, 12, 13 mm a little easier than 3/16, 7/32, 1/4, 9/32, 5/16, 11/32, 3/8, 7/16, 1/2 inch?
Case in point? The above example...